Non-Linear Control

  • Wodek Gawronski
Part of the Mechanical Engineering Series book series (MES)

This chapter discusses three main sources of the antenna non-linear behavior: velocity and acceleration limits, dry friction, and backlash. The velocity and acceleration limits are neutralized by using the command preprocessor, or anti-windup technique. The friction model is presented and the dither is analyzed as a cure for the antenna sticking at low velocities. The backlash model is given and the performance of an antenna with applied counter-torque is analyzed.

Velocity and Acceleration Limits

The antenna control system is shown in Fig.  3.7.Besides the controller, it includes the acceleration and velocity limiters. The acceleration limiters are implemented because the motor currents must be limited to avoid overheating (the currents are proportional to the antenna acceleration). Antenna velocity is limited for safety reasons. Those limits are not affected during normal tracking, but are reached during slew operations. When the limits are reached, the antenna is in a non-linear...


Large Step Friction Torque Motor Torque Applied Torque Wheel Velocity 
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  1. 1.
    Armstrong-Helouvry B, Dupont P, Canudas de Wit C. (1994). Friction in Servo Machines: Analysis and Control Methods. Appl. Mechanics Rev., 47(7): 275–305.CrossRefGoogle Scholar
  2. 2.
    Armstrong-Helouvry B, Dupont, P, Canudas de Wit, C. (1994). A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines with Friction. Automatica, 30(7): 1083–1138.CrossRefMATHGoogle Scholar
  3. 3.
    Bliman PAJ. (1992). Mathematical Study of the Dahl’s Friction Model. European J. Mechanics, A/Solids, 11(6): 835–848.MATHMathSciNetGoogle Scholar
  4. 4.
    Boddeke FR, VanVliet LJ, Young IT. (1997). Calibration of the Automated z-Axis of a Microscope Using Focus Function. Journal of Microscopy, 186 (3).Google Scholar
  5. 5.
    Bridges MM, Dawson DM, Hu J. (1996). Adaptive Control for a Class of Direct Drive Robot Manipulators. Int. J. Adaptive Control and Signal Processing, 10(4).Google Scholar
  6. 6.
    Cai L, Song G. (1994). Joint Stick-Slip Friction Compensation of Robot Manipulators by Using Smooth Robust Controllers. J. Robotic Systems, 11(6): 451-469.CrossRefMATHGoogle Scholar
  7. 7.
    Canudas de Wit C, Olsson H, Astrom KJ. (1995). A New Model for Control of Systems with Friction. IEEE Trans. on Aut. Control, 40(3): 419–425.CrossRefMATHGoogle Scholar
  8. 8.
    Dahl PR. (1976). Solid Friction Damping of Mechanical Vibrations. AIAA J., 14(12): 1675–1682.CrossRefGoogle Scholar
  9. 9.
    Dhaouadi R, Kubo K, Tobise MI. (1994). Analysis and Compensation of Speed Drive Systems with Torsional Loads. IEEE Trans. Industry Applications, 30(3): 760–766.Google Scholar
  10. 10.
    Dupont PE. (1994). Avoiding Stick-Slip Through PD Control. IEEE Trans. Aut. Control, 39(5): 1094–1097.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Dupont PE, Dunlap EP. (1995). Friction Modeling and PD Compensation at Very Low Velocities. J. Dynamic System, Measurement, and Control, 117(1): 8–14.CrossRefGoogle Scholar
  12. 12.
    Edwards C, Postlethwaite I. (1998). Anti-Windup and Bumpless-Transfer Schemes. Automatica, 34(2): 199–210.CrossRefMathSciNetGoogle Scholar
  13. 13.
    Friedland B, Davis L. (1997). Feedback Control of Systems with Parasitic Effects. Proc. American Control Conference, Albuquerque, NM.Google Scholar
  14. 14.
    Gawronski W. (1999). Command Preprocessor for the Beam-Waveguide Antennas. TMO Progress Report, vol. 42-136. Available at http: // .Google Scholar
  15. 15.
    Gawronski W, Almassy W. (2002). Command Pre-Processor for Radiotelescopes and Microwave Antennas. IEEE Antennas and Propagation Magazine, 44(2).Google Scholar
  16. 16.
    Gawronski W, Brandt JJ, Ahlstrom, Jr., HG et al. (2000). Torque Bias Profile for Improved Tracking of the Deep Space Network Antennas. IEEE Antennas and Propagation Magazine, 42(6): 35–45.CrossRefGoogle Scholar
  17. 17.
    Gawronski W, Parvin B. (1998). Radiotelescope Low Rate Tracking Using Dither. AIAA J. Guidance, Control, and Dynamics, 21: 349–352.CrossRefGoogle Scholar
  18. 18.
    Glattfelder AH, Schaufelberger W. (2003). Control Systems with Input and Output Constraints, Springer, London.CrossRefMATHGoogle Scholar
  19. 19.
    Grimm G, Hatfield J, Postlethwaite I et al. (2001). Experimental Results in Optimal Linear Anti-Windup Compensation. Proc. 40 th IEEE Conf. on Decision and Control, Orlando, FL.Google Scholar
  20. 20.
    Hale LC, Slocum AH. (1994). Design of Anti-Backlash Transmission for Precision Position Control Systems. Precision Engineering, 16(4).Google Scholar
  21. 21.
    Hippe P. (2006). Windup in Control, Its Effects and Their Prevention, Springer, London.Google Scholar
  22. 22.
    Ku SS, Larsen G, Cetinkunt S. (1998). Fast Tool Servo Control for Ultra-Precision Machining at Extremely Low Feed Rates. Mechatronics, 8(4).Google Scholar
  23. 23.
    Lee S, Meerkov SM. (1983). Generalized Dither. International Journal of Control, 53(3): 741–747.CrossRefGoogle Scholar
  24. 24.
    Mancini D, Brescia M, Cascote E et al. (1997). A Neural Variable Structure Controller for Telescopes Pointing and Tracking Improvement. Proc. SPIE, vol. 3112.Google Scholar
  25. 25.
    Mancini D, Brescia M, Cascote E et al. (1997). A Variable Structure Control Law for Telescopes Pointing and Tracking. Proc. SPIE, vol. 3086.Google Scholar
  26. 26.
    Mata-Jimenez MT, Brogliato B, Goswami A. (1997). On the Control of Mechanical Systems with Dynamics Backlash, Proc. 36 th Conf. Decision and Control, San Diego, CA.Google Scholar
  27. 27.
    Peng Y, Vrancic D, Hanus R. (1996). Anti-Windup, Bumpless, and Conditioned Transfer Techniques for PID Controllers. IEEE Control Systems Magazine, August, 48–57.Google Scholar
  28. 28.
    Southward SC, Radcliffe CJ, MacCluer CR. (1991). Robust Non-linear Stick-Slip Friction Compensation. J. Dynamic Systems, Measurement, and Control, 113: 639–645.CrossRefMATHGoogle Scholar
  29. 29.
    Stark AA, Chamberlin RA, Ingalls JG et al. (1997). Optical and Mechanical Design of the Antarctic Submillimeter Telescope and Remote Observatory. Rev. Sci. Instrum., 68(5).Google Scholar
  30. 30.
    Tickoo AK, Koul R, Kaul SK et al (1999) Drive-Control System for the TACTIC gamma-ray telescope. Experimental Astronomy, vol.9, no.2.Google Scholar
  31. 31.
    Trautt TA, Bayo E (1999) Inverse Dynamics of Flexible Manipulators with Coulomb Friction or Backlash and Non-Zero Initial Conditions. Dynamics and Control, vol.9, no.2.Google Scholar
  32. 32.
    Tyler SR. (1994). A Trajectory Preprocessor for Antenna Pointing. TDA Progress Report, 42-118, pp. 139–159. Available at: http: // pdf.Google Scholar
  33. 33.
    Yeh TJ, Pan YC. (2000). Modeling and Identification of Opto-mechanical Coupling and Backlash Non-linearity in Optical Disk Drives. IEEE Trans. Consumer Electronics, 46(1).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Wodek Gawronski
    • 1
  1. 1.California Institute of TechnologyJet Propulsion LaboratoryPasedenaUSA

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